Space-based sensors used for missile tracking and space situational awareness (SSA) must be intelligently assigned and slewed to targets for efficient monitoring. Traditional myopic tasking algorithms are not guaranteed to behave well over the long term and do not scale well to complex scenarios with many sensors and targets. On the other hand, optimal solutions to tasking scenarios can be found with exhaustive searches of the solution space, though the search space is combinatoric in nature and thus infeasible to compute at scale. In this research, we approach sensor tasking by constraining the problem space in a unique way that facilitates intelligent behavior without exponential computational complexity. Sensors are constrained to slewing cycles calculated using approximated solutions to the traveling salesman problem. Observation times for each target are then solved simultaneously via convex optimization such that expected error at steady-state is minimized. Two additional heuristics are designed to improve transient error and long-term stability. In experimental simulations, we observe up to 6% lower steady-state root-mean-square error on average than greedy tasking algorithms. Despite being optimized for steady-state error, our algorithm also maintains comparable transient performance to the greedy tasking algorithms when the two heuristics are used.